A semi-analytical solution of Richards Equation for two-layered one-dimensional soil

Aryeni, Tilsa; Ginting, Victor

doi:10.1016/j.advwatres.2022.104199

Cited by 3 publications

(2 citation statements)

References 24 publications

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“…For example, Laplace transformation (Luo G.Y.,2021) [8] ,Boltzmann transformation(Li J. W., 2021) [9] , minimum action principle variational transformation(Zhu Y. L.,2022) [10] , etc.In fact these transformations is a linearized program,which in exchange for the acceptable approximate solution and semianalytical solution(Zhu Y. L.,2022) [11] in the actual engineering by losing a certain accuracy of the equation. However, it is easy to find when reviewing the literature(Aryeni T., Ginting V.,2022;Dolojan N. L. J.,2021;Li L., Ju N.,2020) [12][13][14] .The previous scholars and engineers, may due to the limitation of the academic background, often ignore the preceding mathematical conditions when using various linearization means. For example, in the most widely used linearized Richards equation of Laplace transformation, the premise of the transformation---when t→∞, the question is not discussed that the divergence speed of the original function does not exceed the exponential function in the historical literature.…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Counterexample of Solutions to Unsaturated Infiltration Equations

Zhu,

Chen

2024

Atlantis Highlights in Engineering

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A common method for obtaining the analytical solution of the unsaturated infiltration Richards equation under the first type of boundary condition is the Laplace transform. By linearizing the differential equation through the Laplace transform, solving it, and then applying the inverse transform, the result can be obtained. In this process, the traditional calculation scheme assumes that the original function converges, which is correct in most engineering cases, but theoretically, counterexamples may exist. This article presents a classic counterexample: when the unsaturated infiltration curve has a power-law form, the original integral diverges, resulting in the non-existence of the Laplace transform and the solution of the equation cannot represent the real infiltration situation. Based on this, this article suggests discussing the convergence of the original function before using the Laplace transform to solve the unsaturated infiltration equation to ensure that the results have mathematical significance. The content discussed in this article can be regarded as an improvement and supplement to the traditional unsaturated infiltration calculation scheme.

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Section: Introductionmentioning

confidence: 99%

A Theoretical Counterexample of Solutions to Unsaturated Infiltration Equations

Zhu,

Chen

2024

Atlantis Highlights in Engineering

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“…There are some analytical solutions that can be found in the literature as well 25 . Besides the analytical solutions, semi-analytical 26 , approximate 27 , empirical 28 and even completely arbitrary methods 29 have been developed over the past few decades. However, the complexity of the equation described by Gray and Hassanizadeh 30 leads to further development of numerical solutions; some of these are presented in the literature 31 – 36 .…”

Section: Introductionmentioning

confidence: 99%

From superhydrophilicity to superhydrophobicity: high-resolution neutron imaging and modeling of water imbibition through porous surfaces treated with engineered nano-coatings

Zemajtis

Hasan

Yetik

et al. 2023

Sci Rep

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This paper reports on a superhydrophilic to superhydrophobic transformation of TiO2 nanoparticles doped zinc phosphate coating systems when a hydrophobic agent is applied. The objective of the reported research was to demonstrate the feasibility of a neutron imaging technique for evaluating the performance of the proposed nano-coating system and reveal the differences in water ingress mechanisms which are specific to plain, superhydrophilic, overhydrophobic, and superhydrophobic specimens. The engineered nano-coatings were designed to improve hydrophobic response with inducing the required roughness pattern and introducing the photocatalytic performance. The effectiveness of the coatings was assessed using high-resolution neutron imaging (HR-NI), SEM, CLSM, and XRD techniques. High-resolution neutron imaging revealed that the superhydrophobic coating effectively prevents water ingress into the porous ceramic substrate, whereas water imbibition was observed for superhydrophilic coating during the test duration. The moisture transport kinetics was modeled based on the Richards equation for plain ceramic and superhydrophilic specimens using obtained penetration depth values from HR-NI. SEM, CLSM, and XRD studies confirm the desired TiO2-doped zinc phosphate coatings with increased surface roughness, photocatalytic reactivity, and chemical bonding. The research results demonstrated that a two-layer superhydrophobic system is capable of creating effective water barriers on the surface with contact angles of 153°, which remained effective even after surface damage.

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Effects of biochar addition or grass planting on infiltrations into a sandy soil in the Loess Plateau in China

Wu,

Xu,

Yang

et al. 2024

Earth Surf Processes Landf

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Changing the soil and underlying surface conditions is a key practice for realizing irrigation on‐site storage and infiltration. However, biochar addition and grass planting effects on soil infiltration and water retention capacity remain unclear. The effects of 0% biochar (C1), 1% biochar (C3), 2% biochar (C4), 3% biochar (C5) under ryegrass and 0% biochar (C2), 1% biochar (C6), 2% biochar (C7) and 3% biochar (C8) under Festuca arundinacea on infiltration behaviours were modelled by using sandy loessial soil columns with ‘bare soil + 0% biochar’ as the control (CK). (i) There is a linear relationship between cumulative infiltration and CK–C8 treatment wetting fronts (R2 ≥ 0.982), which showed an initial rising trend and then tended to gradual, and the influence of different treatments was primarily reflected in the middle and late infiltration stages. (ii) Both biochar and grass planting decreased the soil infiltration capacity compared with that of the CK treatment. A high biochar addition rate was beneficial for inhibiting soil water infiltration and improving water retention ability in sandy loessial soil, however, ryegrass soil infiltrabilities under 1%, 2% and 3% biochar were all stronger than that of F. arundinacea. (iii) The cumulative infiltration fitting effects in different treatments with the Kostiakov, Kostiakov–Lewis, Philip, USDA–NRCS, Horton and Green–Ampt equations were all good, although there were some differences in the infiltration rate curves under the six different fitting equations. This study is helpful in understanding effective sandy loessial soil storage ability for irrigation and efficient water resource usage.

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A semi-analytical solution of Richards Equation for two-layered one-dimensional soil

Cited by 3 publications

References 24 publications

A Theoretical Counterexample of Solutions to Unsaturated Infiltration Equations

A Theoretical Counterexample of Solutions to Unsaturated Infiltration Equations

From superhydrophilicity to superhydrophobicity: high-resolution neutron imaging and modeling of water imbibition through porous surfaces treated with engineered nano-coatings

Effects of biochar addition or grass planting on infiltrations into a sandy soil in the Loess Plateau in China

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